The latest study showed 28pc of parents have fallen victim to unexpected costs from app and in-app purchases.

More than eight out of 10 of these claim they receive an increased monthly bill, while 14pc have voiced concerns over affording the costs, and 34pc say they now hide their tablets or smartphones.

However, the study suggested nearly one in five parents give their children their passwords, nearly a quarter of parents do not have a security password, and one in 10 give their children free rein to access whatever content they want.

Meanwhile, more than half of the parents surveyed said they link their smartphone or tablet to an easily accessible subscription service or direct debit account.

Overall, unauthorised purchases have led to an average increase in monthly bills of £34.18 and an estimated total cost of £30,883,157, according to Windows Phone UK, which commissioned the study.

Brett Siddons, of Windows Phone UK, said: "Our research reveals parents are worried about the impact of app and in-app purchases on their bills and we understand the stress this can cause.

"With technology becoming more and more intuitive, it's important that parents can trust in the technology they use and feel as safe as possible when handing over their smartphone and tablet devices to their children."

According to the survey, children spend on average three hours and 21 minutes a week playing games and using apps.

More than 2,000 parents who own smartphones or tablets were consulted for the survey by OnePoll last month.

According to Windows Phone UK, the total figure is a "conservative estimate" and is based on a 50pc penetration for smartphones among the working age population and data from the Office for National Statistics.

Microsoft's Windows Phone 8 offers help for parents to reduce the likelihood of so-called "bill shock". The operating system, introduced last year, comes with a Kid's Corner feature which allows parents to decide what their children can access and prohibits in-app purchases.